Published in Proc European Conf on Visual Perception, Aug 1990.
Images contain information at multiple scales, and pyramids are data structures that represent multi-scale information in a natural way. We discuss a number of types of pyramids that we have applied to a number of applications in image coding and image analysis. The Gaussian and Laplacian pyramids are useful as a front-end representation for many tasks in early vision, and the Laplacian pyramid is reasonably efficient for image coding. Better image data compression can be achieved by using pyramids based on quadrature mirror filters (QMF's), which are closely related to a class of wavelet transforms. QMF pyramids offer a representation that is localized in space and spatial frequency, is self-similar, and is orthogonal. Separable QMF pyramids are quite useful for image coding, but they involve some difficulties with mixed orientations. A QMF pyramid based on a hexagonal sampling lattice exhibits good orientation tuning properties, and is likely to be more useful for general vision applications including models of early vision. We have also explored pyramids based on steerable filters; these pyramids are overcomplete and are less efficient than the QMF pyramids, but offer excellent properties for orientation analysis, image enhancement, and several other tasks. By understanding the strengths and limitations of these representations, we hope to gain insights into the problems confronting both artificial and biological visual systems. Warning: Undefined array key 2 in /System/Volumes/Data/e/1.3/p1/lcv/html_public/pubs/makeAbs.php on line 304
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